图像处理中的数学问题

《图像处理中的数学问题》Introduction、The Image Society、What Is a D来自igital Image、Abo镇想清技改架整理ut Partial Differential Equations(PDEs)、Detailed Plan、Mathematical Preliminaries、How to Read This Chapter、The Direct Method in the Calculus of Vgriations、Topo360百科logies on Banach Spaces、C沙取伯否按帝命以见onvexity and Lower Semicontinuity、Rclaxation、Aboutr-Convergence、The Space of Functions of Bounded Variation、Ba临能述建模凯轴至者sic Defi菜充无美可衡nitions 施阿急on Measures、Definition ofBV(Ω)、Properties ofBV(Ω)、Convex Functions of Measures、Viscosity Solutions in PDEs等等。

• 书名 图像处理中的数学问题
• ISBN 7510005388, 9787510005381
• 页数 377页
• 出版社 世界图书出版公司
• 开本  24开

图书信息

　　出版社: 世界图书出版公司; 第2版 (2009年10月1日)

　　外文书名: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations

　　平装: 377页

　　正文语种: 英语

　　开本: 24

　　ISBN: 7510005388, 9787510005381

来自　　条形码: 978751000360百科5381

　　尺寸: 22 x 15 x 据在结风希阳混伟刘打除1.8 cm

　　重量: 558 g

作者简介

　　作者:(法国)奥伯特(Gjlles Aubert) (法国)Pierre Kornp杆待活求绿水却掉振初robst

目录

　　Foreword

　　Preface to the Second Edition

　　Preface to the First Edition

　　Guide t波军跳培右雨板味食房信o the Main Mathematical Concepts and

　　Their Application

　　Notation and Symbols

　　1 Introduction

　　1.1 The Image Soci构ety

　　1.2 What Is a Digital Image7

　　1.3 About Partial Differential Equations(PDE脚益于便伤燃段士s)

　　1.4 Detailed Plan

　　2 Mathematical Preliminaries

　　How to Read Th规高议互农开is Chapter.

　　2.1 The D来自irect Method 怀安手武掉杆刑连in the Calculus of Vgriations

　　2.1.1 Topologies on B360百科anach Spaces

　　2.1.2 Convexity and Lower Semic冲质垂才续呢功依ontinuity

　　2.1.3 Rclaxat.ion

　　2.1.4 About r-Convergence

　　2.2 The Space of Functions of Bounded Variation

　　2.2.1 Basic Definitions on Measures

　　2.2.2 Defi了nition ofBV(Ω)

　　2.2.3 Properties ofBV(Ω)

　　2.2.4 Convex Functions of Measures

　　2.3 Viscosity Solutions in PDEs

　　2.3.1 About the Eikona原层地养至向权l Equation

　　2.3.降概应关损2 Definition of V英找经亚构老策船浓奏程iscosity S滑足言倒素刻酒走研财践olutions

　　2.3.3 About the 触Existence

　　2.3.4 About the Uniqueness

　　2.4 Elements of Differential Geometry:Curvature

　　2.4.1 手且敌Parametrized Curves

　　2.4.2 Curves aS Isolevel of a Functio烟n u

　　2.4.3 Images aS Surfaces

　　2.5 0ther Classical Results Used in This Book

　　2.5.1 Inequalities

　　2.5.2 Calculus Facts

　　2.5.3 About Convolution and Smoothing

　　2.5.4 Uniform Convergence

　　2.5.5 Dominated Convergence了heorem

　　2.哪贵列之啊京增5.6 Well-Posed Problems

　　3 Image Restoration How to Read This Chapter

　　3.1 Image Degrada布扩斤花经似领tion

　　3.2 The Energy Meth威od

　　3.2.1 An Inverse Problem

　　3.2.2 Regularization of th细离若投说e Problem

　　3.2.3 Existence and Uniqueness of a Solution for the Minimization Problem

　　3.2.4 Toward the Numerical Approximation

　　The Projection Approach

　　The Half-Quadratic Minimization Approach

　　3.2.5 Some Invariances and the Role of

　　3.2.6 Some Remarks on the Nonconvex CaSe

　　3.3 PDE-BaSed Methods

　　3.3.1 Smoothing PDEs

　　The Heat Equation

　　Nonlinear DiRusion

　　The Alvarez-Guichard-Lions-Morel

　　Scale Space Theory

　　Weickert's Approach

　　Surface Based Approaches

　　3.3.2 Smoothing-Enhancing PDEs

　　The Perona and Malik Model

　　Regutarization of the Perona and Malik Model:Catte et aL

　　3.3.3 Enhancing PDEs

　　The Osher and Rudin Shock Filters

　　A Case Study:Construction of a Solution by the Method ofCharacteristics

　　Comments on the Shock-Filter Equation

　　3.3.4 NeighborbOOd Filters，Nonlocal Means Algorithm，and PDEs

　　Neighborhood Filters

　　How to Suppress the Staircase Effect?

　　Nonlocal Means Filter(NL-Means)

　　4 The Segmentation Problem

　　How to Read This Chapter

　　4.1 Definition and Objectives

　　4.2 The Mumford and Shah Functional

　　4.2.1 A Minimization Problem

　　4.2.2 The Mathematical Framework for the Existence of a Solution

　　4.2.3 Regularity of the Edge Set

　　4.2.4 Approximations of the Mumford and Shah Functional

　　4.2.5 Experimental Results

　　4.3 Geodesic Active Contours and the Level.Set Method

　　4.3.1 The Kass-Witkin-Terzopoulos model

　　4.3.2 The Geodesic Active Contours Model

　　4.3.3 The Level-Set Method

　　4.3.4 The Reinitialization Equation

　　CharaCterization of the Distance Function

　　Existence and Uniqueness

　　4.3.5 Experimental Results

　　4.3.6 About Some Recent Advances

　　Global Stopping Criterion

　　Toward More General Shape Representation

　　5 Other Challenging AppliCations

　　How to Read This Chapter

　　5.1 Reinventing Some Image Parts by Inpainting

　　5.1.1 IntroduCtion

　　5.1.2 Variational Models

　　The Masnou and Morel Approach

　　The Ballester et al.Approach

　　The Chan and Shen Total Variation Minimization

　　Approach

　　5.1.3 PDE-Based Approaches

　　The Bertalmio et a1.Approach

　　The Chan and Shen Curvature-Driven Diffusion Approach

　　5.1.4 Discussion

　　5.2 Decomposing an Image into Geometry and Texture

　　5.2.1 Introduction

　　5.2.2 A Space for Modeling Oscillating Patterns

　　5.2.3 Meyer'S Model.

　　5.2.4 An Algorithm to Solve Meyer'S Model

　　Prior Numerical C:ontribution

　　The Aujol et a1.Approach

　　Study of the Asymptotic Case

　　Back to Meyer's Model

　　5.2.5 Experimental Results

　　Denoising Capabilities

　　Dealing With Texture

　　5.2.6 About Some Recent Advances

　　5.3 Sequence Analysis

　　5.3.1 Introduction

　　5.3.2 The Optical Flow:An Apparent Motion

　　The Optical Flow Constraint(OFC)

　　Solving the Aperture Problem

　　Overview of a Discontinuity.Preserving

　　Variational Approach

　　Alternatives to the OFC

　　5.3.3 Sequence Segmentation

　　Introduction

　　A Vriational Formulation

　　Mathematical Study of the Time-Sampled Energy

　　Experiments

　　5.3.4 Sequence Restoration

　　Principles of Video Inpainting

　　Total Variation(tV)Minimization Approach

　　Motion Compensated(MC)Inpainting

　　5.4 Image Classification

　　5.4.1 Introduction

　　5.4.2 A Level-Set Approach for Image Classification

　　5.4.3 A Variational Model for Image Classification and Restoration

　　5.5 Vector-Valued Images

　　5.5.1 Introduction

　　5.5.2 An FXtended Nbtion of Grudieut

　　A Introduction to Finite Digerence Methods

　　B Experiment Yourself!

　　References

　　Index